Verse 2 & 3

ٱلْحَمْدُ لِلَّهِ رَبِّ ٱلْعَـٰلَمِينَ

ٱلرَّحْمَـٰنِ ٱلرَّحِيمِ

Alhamdulillahi Rabbil-Aalameen

Ar-Rahmaan-ir-Raheem

Praise be to Allah, the Lord of the worlds

The Most Gracious, the Most Merciful

Alhamdulillah - Praise be to Allah.
This refers to praising Allah for the attributes of perfection and for His actions that are based on generosity and justice. So to Him be perfect praise in all ways.

Rabbil-Aalameen - The Lord of the worlds
The Lord is the One Who sustains all creatures - which refers to all beings other than Allah - because He created them, granted them everything that they need and bestowed great blessings upon them; if they were deprived of those blessings they would not be able to survive, for whatever blessings they enjoy come from Him. 

He sustains His creation in two ways, general and specific. In general terms, this refers to His creation o f all creatures, His granting o f provision to them and His guiding them to that which is in their best interests, which enables them to survive in this world.

In specific terms, it refers to His cherishing o f His close friends, by means o f instilling faith in their hearts, guiding them to it, perfecting it for them and warding off from them distractions and obstacles that come between them and faith. In real terms, this means guiding them to everything that is good and protecting them from everything that is bad. Perhaps it is for this reason that most o f the supplications o f the Prophets used the word Lord (Rabb),3 since all their requests and needs came under His special cherishing.

The phrase "the Lord of the worlds" indicates that He alone has the power to create, and He alone controls His creation, bestows blessings and is completely independent o f means, whilst all o f creation is dependent upon Him in all respects.