Well, the smell is caused by bacteria living in and around the sweat glands and hair in your armpits. All of us get this odor causing bacteria after puberty, and actually the sweat glands and hair there is supposed to promote the growth of such bacteria so the smell is stronger. Once upon a time in our evolution, that scent was attractive to the opposite sex (some say it still is in small amounts).
Anyway, these days that odor is socially unacceptable in most societies (right or wrong, its just the norm). You've got two options to eliminate or cover up armpit odor besides regular bathing: Deodorants only cover up the odor, and inhibit the growth of the odor causing bacteria. For most conditions and people, this is good enough protection against odor. However, under times of stress, heat, and sweat, deodorants may not be good enough. They also rarely last for more than 24 hours between application. Next strength defense against odor is an anti-perspirant/deodorant, which has the odor masking properties of the deodorant, but also applies a chemical to the skin to prevent sweating. Less sweating = less moisture = less bacteria growth to create odor. Effectively, the chemical seals off the sweat pores in the skin. Some people get itchyness from anti-persperants, caused by the pores having trapped sweat in them, or an allergic reaction to the chemical (some derivative of zinc). I itch like crazy if I use an anti-persperant, and thus I only use deodorant, even though its not as effective at preventing odor.
So, your options are to first try an anti-persperant. If you itch from it, then switch back to a deodorant, but try a different brand. Some are better than others at preventing odor.