When your body sweats it mixes with the dirt collected on your skin throughout the day to cause itchy armpits.
When exercising you should wear loose clothing to give your armpits the chance to breathe and prevent rubbing against your skin.
Bacteria is an irritant and is one of the biggest causes of underarm itchiness, so try to spend a little more time on hygiene in your armpits. When your skin is wet it's much easier for bacteria to collect and spread, and once this happens your skin is susceptible to infections that cause things like itchy armpits.
Shaving without a moisturising cream or gel, with a dull razor, or even too often, can all cause itchy armpits.