The Nanosuit has four basic functions: Armor, Speed, Strength, and Cloak Modes.
Armor
In Armor Mode, when you are hit, suit energy drains instead of your health. Be warned however, that when suit energy runs out, you start losing health. If you are not playing stealthly, then this mode is probably the safest to be in. If you are playing stealthly, then this is the suit mode recommended for replenishing depleted Cloak energy.
Speed
As the name suggests, this mode allows you to move around faster than normal. Walking (and swimming) speed is increased at no cost to suit energy, but sprinting in Speed Mode drains the energy bar very rapidly, so use it in short bursts. This mode also allows you to jump further, unlike Strength mode, which makes you jump higher. Melee attack speed is also increased at the cost of energy.
Strength
In Strength mode, you have increased... well... Strength. You can throw soldiers, objects (and chickens!) further, and throwing soldiers in Strength Mode is lethal to them. Strength mode enables you to jump higher, as opposed to Speed Mode, which makes you jump further.