О́чень: very, really, incredibly
Очень (very) is one of those handy little words you learn in Russian 101 and then use every day. Add it to any verb to jack up the intensity and emotion. For example: Я тебя люблю (I love you) is a summer fling; я тебя очень люблю (I love you very much) is maybe we should think about a mortgage.
Say it on its own to telegraph strong feeling. Торт понравился? Очень. ("Did you like the cake?" "Very much.") Or combine it with need to turn a statement into a plea: Нам очень нужно их пригласить! (We really, really have to invite them!)
But ubiquitous as it is, очень is not the only way to express very-ness. You want very? Russian's got lots of very — a varied assortment providing a special very for every situation.
One batch of very starts with "without" (без) and is good for describing something that is so very, very big it seems boundless. Он безгранично щедрый. (His generosity knows no bounds.) Я безмерно горжусь. (I'm bursting with pride.) Она бесконечно благодарна (She'll be eternally grateful).
Another batch is for something that's so very, very whatever you just can't believe your eyes. Он невероятно красив. (He is unbelievably handsome.) Несколько часов они убирались, устали неимоверно. (They spent hours cleaning and were just exhausted.) Я безумно люблю клубнику. (I adore strawberries, literally "I love them madly.") Волжская дамба — необыкновенно важный объект. (The Volga dam was an extraordinarily important project.)
And then there are the awfully, terribly verys, which can be used to describe things that are intensely bad or insanely good. Я жутко люблю жизнь. (I love life so terribly much). Ужасно хочется сладкого. (I have an awful craving for something sweet.) Жуть как хочется сладкого. (I'm dying for a sweet, literally "It's awful how much I want a sweet.") Мы видели, как кошмарно пьяный Борис шёл домой. (We watched how Boris, horridly drunk, walked home.) Он послал его не шибко грубо. (He told him where to get off, but he wasn't terribly rude about it.)
It's fun to see the horribly, terribly verys going both ways: Я-то клевер предпочитаю. Уж больно он вкусный. (Me — I prefer clover. It's delicious, literally "it's painfully tasty.") Речка им больше не попадалась, а вода из-подо мха казалась больно противной. (They didn't come across any other rivers, and the water from under the moss tasted just horribly bad.)
And it's very satisfying to use the amazingly, fantastically verys, where something is so very, very out of the world. Он фантастически богат. (He is fantastically wealthy.) У неё феноменально зелёные, тигриные глаза. (She has phenomenally green tiger's eyes.) Шеф повар изумительно вкусно готовит. (The chef cooks amazingly well.)
Russian, being Russian, has a few little tricks up its linguistic sleeve with очень. In Russian collective experience, you can have too much of a good thing. For example, Он очень умный could simply mean that a guy is really smart. Or it might sound like it's going to be followed by "но …" ("but …") And if you switch word order, он умный очень almost always means: He's too smart for his own good. And if, God forbid, someone is слишком умный (way too smart), that means his intelligence has gotten him in trouble.
Russians have a phrase for that, too: Горе от ума (Woe from Wit).