Istinjā` is washing yourself after relieving yourself in the toilet. This is of course very important for the purpose of tahārah, wanting to pray, etc.
However, there is something else that is important to do, but is not obligatory, and that is istibrā`. Istibrā` is clearing the urinary outlet after urinating. For a male, you do this by what we call the nine squeezes.
The advantage of istibrā` is if you do it, with any discharge you might feel after the istibrā` and the istinjā` , you consider it to be tahir. However, if you do not do the istibrā`, and you experience a discharge, not knowing what it is, you deem it as najis, and you must wash yourself again.
I have added a link to a recorded lesson on this, with detailed explanation.
And Allah knows best.
Istinja means ritually cleaning your private parts after using the toilet. It is not obligatory to do Istinja immediately but only for performing Prayers (Salah) or Tawaf around the Ka'bah as one of the conditions of Salah to be ritually pure (Taahir) in your body and clothes. If you use the toilet and did not do Istinja, it is permissible to wait till the time when you want to perform Salah and do Istinja before Salah. Even your Wudhu is valid before doing Istinja because the parts of Wudhu only should be Taahir while performing Wudhu and not all the body. All body Must be Taahir for Salah and Tawaf.
It is ok only to be ritually pure before salat and other acts that require ritual purity (such as tawaf around the Ka'bah).
However it is good to be clean as much as possible, if it is possible.