What is meant by learning by heart the beautiful names of Allah, may He be exalted
Question

What is meant by the phrase “whoever learns them by heart will enter Paradise”?.
Praise be to Allah.Al-Bukhaari (2736) and Muslim (2677) narrated from Abu Hurayrah (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “Allah has ninety-nine names, one hundred less one. Whoever learns them by heart will enter Paradise.” 
“Learning by heart”, which is mentioned in the hadeeth, implies the following: 
1.Memorising them
2.Understanding their meaning
3.Acting in accordance with the meanings. So if a person knows that He is One, he does not associate anything else with Him. If he knows that He is the Provider (ar-Razzaaq), he does not seek provision from anyone other than Him. If he knows that He is Most Merciful (ar-Raheem), then he does acts of obedience and worship that are the means of attaining this mercy… and so on.
4.Calling upon Him by these names, as He, may He be glorified and exalted, says (interpretation of the meaning): “And (all) the Most Beautiful Names belong to Allah, so call on Him by them’ [al-A‘raaf 7:180]. So he might say: O Most Merciful (Ya Rahmaan), have mercy on me; O Oft-forgiving (Ya Ghafoor), forgive me; O Accepter of repentance (Ya Tawwaab), accept my repentance, and so on.
Shaykh Muhammad ibn Saalih al-‘Uthaymeen said: Learning them by heart does not mean writing them down on a piece of paper then repeating them until one has memorised them. Rather what it means is:
Firstly: learning how to pronounce the names
Secondly: understanding their meanings.
Thirdly: worshipping Allah in accordance with what they signify, which involves two things:
(i)Calling upon Allah by them, because He, may He be exalted, says (interpretation of the meaning): “… so call on Him by them” [al-A‘raaf 7:180], to that they may become a means of attaining what you seek, so choose a name that is appropriate to what you seek. When asking for forgiveness, say: O Oft-forgiving (Ya Ghafoor), forgive me. It is not appropriate to say: O You Who are stern in punishment (Ya Shadeed al-‘Iqaab), forgive me; rather that is more akin to mockery. What you should say (if you call upon Allah by this name) is: Save me from Your punishment.
(ii)In your acts of worship you should do is what is implied by these names. What is implied by the name ar-Raheem (Most Merciful) is mercy, so do righteous deeds that will bring the mercy of Allah. This is what is meant by learning them by heart; if it is done like this, then it deserves to be the price of admission to Paradise. End quote. 
Majmoo‘ Fataawa wa Rasaa’il Ibn ‘Uthaymeen, 1/74 
And Allah knows best.