This is the 連用形 (Renyoukei, continuative form or linking form), which is used when you combine verbs with other endings (-masu, -tai, ...) or when you make a compound verb. It's also used for nouns that are derived from verbs.
Sometimes it's also used to link sentences, similar to -te, but I haven't figured out the exact rules for that. Maybe some native speakers can explain the details.
See e.g. http://en.wikipedia.org/wiki/Japanese_grammar#Stem_forms for the other forms.