It's not because people in Russia value money that much, even while they do. Neither it is any sort of money laundering. The sole reason being - many people have no idea how to make good gifts.
Making a good present to a person is both a commitment and a sign of valuability of the person gifted. It's an art which is not lost but, instead, well-hidden in relationships between people who love and respect each other. Many people, while feeling obligated to make a present - otherwise, in our status-driven society (that, at least, I'm an unwilling partaker of), people will assume your resentment for the giftee - can't make it enough of a commitment to spend their time and money on things that may actually be valued. What if you're wrong, and you gift something of little interest or, even worse, disgrace? What if the giftee will not appreciate it? This is going to be a disaster!
Which is why people opt for money.
Money give the giftee a freedom of choice they didn't think they wanted or needed. It's a way of saying "I have no idea what to give you, so take this as a supposed sign of appreciation". Granted, people don't gift money when they don't like the person (often), but the disconnect between the idea of a gift - a surprise item that ought to fit its recipient - and the idea of a money gift might strike one odd if they aren't used to such a tradition.
Children are given a small amount at first: a hundred rubles at first (which is a pack of Pringles or a single pirated DVD), then two hundred, then three, five. Teenagers might even get a thousand rubles, which compares to a good book with some change left, then two or even three. Maybe richer families have it more generous, but for where I am, three thousand rubles is the upper limit for a money gift from a single person or a family (which is equally often and perfectly acceptable). Often, money gifts are accompanied by a chocolate bar.
Money gifts are given in an envelope. I believe it stems from the idea that one should never tell how much money were gifted to one person so that anoter won't become jealous; apparently, it's part of the culture to operate within such immature boundries. The chocolate bars, as well as the birthday cards handwritten (often alongside the generic, printed congratulation - it might be hard to find a cleaner card), often reside in the same envelope, which isn't supposed to be named, given how people ought to remember which packages belong to which person (it's often the case that families don't meet until most or everybody can gather, so the gifts from previous holidays wait by the gifter).
If you want to show that you love the person gifted to, you'd choose something they care about. It doesn't have to be big or expensive, but it's a far better touch than any amount of money one might be gifted instead. Sometimes, such presents are cheesy - like a plastic "Best father" medal my friend gifted once, along with something more serious (joined forces with her mother) - but it still might be appreciated more than cash.