It means exactly that. It works like this.
Under the Fifth Amendment to the US Constitution, no-one can be compelled to give evidence against himself. So if a grand jury is investigating a complaint and you are hauled before it to testify, you can refuse to testify if your evidence would incriminate you.
The DA can deprive you of this protection by granting you immunity from prosecution (even if you have not asked for it). Since you cannot now be prosecuted, you have no basis for refusing to give evidence.
In practice, of course, the DA will only do this if he is bloody sure that you have evidence which will secure the conviction of someone else. So (a) it’s generally only the small fry who are granted immunity and (b) it is usually by agreement, since they have already told the DA what evidence they are willing to give in return for immunity, and © it may be part of a bigger deal where you are granted immunity on more serious charges and have a plea-bargain on lesser charges and (d) as Polycarp has noted, you can still be sued in relation to the same matter, notwithstanding your immunity from civil prosecution.