On my arm/upper body exercises I lift up to 70 lbs., especially for triceps. For things like preacher curls I can lift up to 50 lbs. I started out around 10 lbs. for preacher curls, 20 lbs. for lat pulldowns, now I'm up to I guess an ave. of 50 lbs. overall. Obviously I have gained strength, but is this considered heavy? It's such a relative term.
The actual weight numbers do not really equate to whether you are "lifting heavy." What matters is what those weight numbers represent in terms of a percentage of a max effort.
Someone who does 3 sets of 12 @ 80lbs when they could do 3 sets of 12 @110 lbs or 3 sets of 8 @ 130lbs is not lifting heavy while someone who may only be lifting 50lbs but is doing 3 sets of 8 and is approaching failure on that last rep is lifting heavy despite a lighter actual weight than the first person.
I don't think there is a set definition of lifting heavy. For me, doing sets of anwhere from 1 to 8 reps at 80% or more of 1 rep max is "lifting heavy."
Whether you are lifting "heavy enough" really depends upon your goals.
What is heavy enough for someone looking for Muscular endurance and what is heavy enough for someone focusing on increasing strength are two entirely different things (with those looking primarily for hypertrophy falling in the middle). Let the goal determine the rep/set scheme and then make sure that you are training to or close to failure on that last set and you will be fine (you don't always have to go to failure but you do want to make sure that you are not frequently "leaving too many reps in the tank).
If you are unsure of your goals and what set/rep scheme to use, follow Nelie's advice and you will get a nice a hypertrophy response with some strength and endurance benefits as well.
Actually I should modify that in saying the last set reaching failure between 6-10 reps but it is really something personal I think. I usually try to go to failure on my second to last and last set, last set reaching failure around 6 reps.
I have a related question. Generally, if I start failing in the second set, I'll go down a smidge on the weight for the 3rd set, on the principle that it's better to do 3x10 even with a lower weight at the end, than to only manage 6 or 8 on the third set. Am I mistaken about this? Does it matter?
Baffled, That is an excellent question. One for which I do not have a definitive answer.
I have seen various opinions on this, including some that seem bogus and farfetched, such as one (I forgot from whom) that stated that if you do your last set with a lighter weight, your muscles will remember that weight the most and the adaption will be based on that weight. Thus if you use 30lbs for the last set, your body will adapt only to the point required to lift 30lbs. If find this opinion unreasonable. What if I lift a jar of pickles after my workout, will my body fail to adapt because it is already strong enough to lift a jar of pickles?
I do have an opinion, for what it's worth: I would look at the total amount of work performed. Say you are doing an exercise with 100 lbs. You do 2 sets of 8 and then fail at 6 reps on the third set for 2400 total pounds. If you drop the weight on set 3 to 80 lbs to do the 8 full reps then you are doing 2240 lbs. You are doing less work. However, if you fail at 5 reps with the 100lbs on set three for 2300 total pounds and can decrease the weight drop to 90lbs for set 3 and do the full eight, you are doing 2320 or 20 lbs more total. I'd evaluate whether dropping the weight in that manner and do the one that allows me to do the most total weight. That is in most circumstances. Obviously, if I am doing higher reps because part of my goal is to increase muscular endurance, then I would do whatever is necessary to achieve the total reps needed.
What if I lift a jar of pickles after my workout, will my body fail to adapt because it is already strong enough to lift a jar of pickles?
That's funny. I picture my muscles immediately giving up and atrophying after I get home from the gym and pick up a saute pan in which to make scrambled eggs.
The total weight scheme sounds fairly reasonable. I shall have to do some math.
Thanks for the input.
What if I lift a jar of pickles after my workout, will my body fail to adapt because it is already strong enough to lift a jar of pickles?
I love that!
Baffled , I use the "total work" approach on some exercises and the "when I've hit failure, I'm done" approach on others. There are a lot of exercises I just don't want to go to failure on. I no longer have a totally reliable spotter for bench presses and my chest (not including boobage) is plenty big. I don't lift to failure when I do presses. Same with shoulder presses. I'd like bigger shoulders, but I'd also like to keep my tendons intact. Squats are another exercise I will no longer due to failure. I don't go to failure on barbell clean and presses. I like my teeth in my mouth and my jaw intact. Getting injured is really counterproductive. For those, I do a work expenditure type scheme.
Push ups and pull ups, on the other hand, are quite safe to do to failure. Not too many ways to get hurt unless you REALLY fail at a push up and need dental work! Same with lunges. You aren't going to land in a heap with a pile of metal on top of you.
Today I used machines for the first time in ages to do lat pull downs and seated cable rows. I went to failure on both because it is completely safe (and it's wierdly fun to let the lat bar pull ME up in the air on the last rep that I can do!).
What is considered lifting heavy?
That's funny. I picture my muscles immediately giving up and atrophying after I get home from the gym and pick up a saute pan in which to make scrambled eggs. 
I love that!