Rashi comments based on the medrash that גרתי = תרי"ג and therefore Yaakov was saying to Esav, even though I lived in Lavan's house I kept all 613 mitzvos.
However, there is an obvious question here. No one can actually keep all 613 mitzvos. Some mitzvos are just for Cohanim, some are just for the Cohen Gadol, some just for the King, some just in Israel, etc. Therefore, how could Yaakov say he kept all 613 mitzvos? Additionally he clearly didn't keep all 613 mitzvos because he married 2 sisters.
There are a number of answers I will mention 2.
1. Yaakov was referring to those mitzvos that are שקולה כנגד כל המצות, like talmud torah, tzitzis, etc. He meant that he kept those mitzvos and therefore it was as if he had kept all 613.
2. By the ברית בין הבתרים Avraham asks Hashem based on what will his children be זוכה? Hashem answered בזכות הקרבנות. Avraham then asked, what about when there is no Beis Hamikdash and no קרבנות? Hashem answered that if we say (learn) the קרבנות it is considered as if we were מקריב them. This is why we daven musaf on Shabbos and Yom Tov and mention the Musafim, ונשלמה פרים שפתינו.
As an aside, based on this RHS says that if you come late to shul it is better to say all of קרבנות and skip in פסוקי דזמרא, then skip קרבנות because קרבנות is a קיום דאורייתא while פסוקי דזמרא is just a nice thing.
Some acharonim say that this is not just a din by קרבנות but it applies to other parts of Torah as well. Whatever mitzva you personally cannot fulfill, if you learn the dinim of the mitzva it is as if you fulfilled the mitzva. Based on this, Yaakov was telling Esav that whatever mitzvos he could keep he kept, all the rest he learned the dinim and it was as if he kept them as well.