It is stated in the Talmud (Brachos 4b) that one who recites "T'hila L'David" three times a day secures their place in Olam Haba. Why is this? What is so special about this psalm that it would guarantee such a reward? Furthermore, why specifically three times?
The Talmud says:
Rabbi Elazar said that Rabbi Avina said: Anyone who recites: “A Psalm of David” (Psalms 145) three times every day is assured of a place in the World-to-Come. What is the reason? Because it is arranged alphabetically [and] because it contains praise for God giving sustenance to all living creatures: “You open Your hand and satisfy every living thing with favor” (Psalms 145:16). [Berakhot 4b]
Concerning that prayer, the Mishnah Berurah (1:13) writes:
It's not enough to just read them, but one should contemplate what he's saying and recognize the wonders of Hashem.
Why this MA? Machatzis ha'Shekel is brought down by Rabbi Mordecai Kornfeld from Kollel Iyun Hadaf, Yerushalayim in saying:
Through saying Tehilah l'David with intent, he will recognize some of Hash-m's Chesed and greatness. This will make him zealous to fulfill Hash-m's word and guard himself from sin. If he sinned, he will repent fully. Through this, he merits the world to come.
The ArtScroll gemara Brachos cites the MB and brings the Rabbeinu Bahya on Vayikra 7:37:
What the sages mean is that once one has familiarized himself with the deeper meaning of each type of offering, it enables the student of these laws to gain new insights which in turn will strengthen his resolve to meticulously observe all the precepts of the Torah. Seeing that offering the sacrifices is also meant to bring us closer to G’d, it is no more than reasonable that studying these laws will have a similar effect. Such study and new resolve to observe the Torah will result in the sins of such people being forgiven, similar to their having performed the actual procedure of offering the relevant sacrifices.
Bonus: See the Meshech Chochmah, beginning of parashas Bechukosai.
In a footnote, ArtScroll explains:
The Gemara does not mean that one merits a place in the World to Come merely due to the recital of this psalm. Rather, it means that it could be a decisive factor (Ohel Moed, cited by Beis Yosef to OC 51). In other words, the recital of this psalm is not a matter of minor importance. It ranks in importance among all other mitzvos, and is thus weighty enough to tip the scale in someone's favor and merit him with his place in the World to Come (Avudraham, in his discussion of the Ashrei recited after the Shemoneh Esrei)
According to all of the above, it has to do with the fact that due to this prayer(s), we can see how we are meant to behave ourselves during the day, following the morning-prayers. The Kollel Iyun Hadaf article explains, in the name of the Rabbeinu Yonah:
Two explanations are given by TALMIDEI RABEINU YONAH. Both explanations assume that it is not simply following the order of the prayers that earns one a share in Olam ha'Ba. One will achieve this lofty level only if he follows the mention of the redemption with the Shemoneh Esreh prayer for the proper reasons. If one continues and conducts himself throughout the day in accordance with the principles inherent in the reasons for the connection between the account of the Exodus and the Shemoneh Esreh, he will be worthy of the World to Come.