Muscles grow from training by breaking down and then rebuilding stronger than before to prevent future breakdown, basically. Hence you need enough protein to repair the damage and a bit extra for the reinforcement.
Train without enough protein and you get the breaking down bit without the protein to repair, ie you can actually lose lean muscle tissue.
Some proteins the body can manufacture itself from other food sources but not the 'essential' amino acids, which must be obtained directly from your diet.
If you are a vegetarian or vegan there are many ways to get sufficient amounts of protein in your diet.
Many vegetarians eat fish and eggs - problem solved
Vegans - there is tofu, soy. Then you can do thinks like nuts and rice together, grains and beans together etc.. The combining of the different foods will give you the protein you need.
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Vegan diets are very tough to stick to as a diet choice - much easier if a moral thing as well. Having said that it can be a choice worth sticking to as I've known people just shrug off excess fat having gone vegan.
It's even tougher as a bodybuilder when protein requirements are way above normal but if the veggie life is the reason for the question my answer would be "It's not a good enough excuse, you need the protein and it is possible". There are plenty of vegan bodybuilders out there.
If it's nothing to do with vegetarianism and you just can't get hold of protein shakes or have time to cook then a couple of boiled eggs are a start and better than nothing.