Somebody (Mark Twain?) once said that if you don't like the weather around here, wait a minute. It's true. A blizzard can be followed two days later by 70-degree days (and oh, what a mess that leads to!).
In general, however, Boston's climate is similar to New York's. Expect hot, humid days in the summer (but don't be surprised if you get here and it's fairly cool) and snow in the winter. Winter temperatures tend to hover around freezing - we rarely get extended periods of Minnesota-like freeze-your-ears-off blasts (but it has happened). Boston tends to have a January thaw. Springs and falls are mild, but spring often seems to last for only three or four days - on Monday it's freezing, then it gets nice, then blammo, summer hits.
Confused? Probably your best bet when planning a Boston trip is to think layers. If the weather warms up, you can peel things off; if it gets cold, just slap another layer or two on.
You can get more specific weather info (including current forecasts) on Weather page.