It's from Julius Caesar - but you probably know that by now.
It's one of the conspirators trying to persuade a friend of Caesar to join (or maybe renew his allegiance to - it's a long time since I read it) the conspiracy; or maybe it's a soliloquy (Brutus?) in which the speaker is trying to persuade himself to do it. He says that in human dealings ('the affairs of man') there is a tide. The image is based on ships leaving the safety of a harbour: 'the flood' is when the tide is at its deepest. He goes on to say 'we must take the current when it serves' - in other words, we must take advantage of favourable conditions while we can. There a couple of sayings, with the same effect:
Strike while the iron is hot (think of a blacksmith)
What confused me was this combination – the flood, which I only referred to rivers (or rains) and the tide. So, the flood is, metaphorically, a moment of opportunity which you must seize before the tide takes it back to sea.
There is a tide in the affairs of men,
Which, taken at the flood, leads on to fortune;
Omitted, all the voyage of their life
Is bound in shallows and in miseries.
You may have had trouble parsing 'Omitted' in that context. It's rather dense language. '[If the tide is] omitted [that is, if the people involved don't take advantage of it], all the voyage of their life [that is, the life of those people] is bound in [restricted to] shallows [areas of the sea where the water is too shallow for a ship to move freely]...'.