Basically prayer serves a couple of purposes-
1- Power Download.
Just a few words mumbled now and again when we're knackered such as "Jesus remember me" is enough to log us onto God and give us an immediate power download to buck us up.That's what nonchristians can't understand, christianity WORKS like it says on the box, which is why it's become the biggest religion on the planet.
".. our gospel came to you not simply with words, but also with power.." (1 Thess 1:5)
"My Christian faith has been such a backbone through so many difficult times,for me Christianity is about being strengthened"- Bear Grylls
http://www.alphafriends.org/news/bear-grylls-my-faith-quite-simple
2- Reality-bending
Prayer for those who are ill or in danger is a kind of thought-pressure that can affect this illusion we call 'reality'.
"You can say to this mountain, 'Go, throw yourself into the sea,' and it will be done"-Jesus in Matt 21:21
Of course prayer effects are usually much more subtle and might go unseen until they kick in days, weeks, months or even years down the line.
'Reality' can also be regarded as a 'dream' as well as an illusion, and dreams can be manipulated by thought-pressure (prayer)..
"You can be in my dream if i can be in your dream" -Bob Dylan
"Strawberry Fields...nothing is real" - The Beatles
"Our revels now are ended. These our actors,
As I foretold you, were all spirits and are melted into air, into thin air;
And, like the baseless fabric of this vision,
The cloud capped towers, the gorgeous palaces,
The solemn temples, the great globe itself,
Yea, all which it inherit, shall dissolve,
And, like this insubstantial pageant faded, leave not a rack behind.
We are such stuff as dreams are made on,
and our little life is rounded with a sleep"
- The Tempest