Verified answer

Mana always empty between steps and phases.

Say you are tapping mana on your first main phase and doesn't use it and moving to combat phase then that mana will simply disappears. With omnath, you can store green mana in your mana pool indifinitely as long as he is in the battlefield. So you can tap for mana in your main phase and move through steps and phases and that mana is still there. You can even store mana to use for your next turn combining it with that turn's mana to cast a big spell.

Fully explained, Omnath, Locus of mana allows you to float green mana in your mana pool as steps and phases end (usually it empties out at that time even if you hadnt used it) and he gets a +1/+1 buff for each green mana in your mana pool. this mana can be used at any time for any reason but remember that omnath will loose 1 buff per mana spent from your mana pool. note that this only works for green mana and that if omnath somehow gets killed (say on their first main phase they kill him) then you still have all that green mana untill you both pass priority and his first main phase ends.

It's mana LOCUS.

Omnath, the mana locus acts like a mana holder and it gains +1/+1 for every green mana in your mana pool. If something happens tot he locus, like a doom blade, all that stored mana has to be used by the end of the step or it disappears.