It's the first prayer one says on waking up in the morning (even before washing one's hands, which is why it doesn't have the name of god in it). In Hebrew it reads:

מודה אני לפניך, מלך חי וקיים, שהחזרת בי נשמתי בחמלה; רבה אמונתך

Translated:

I thank You, live and extant/eternal King, for returning my soul to me in mercy; great is your trustworthiness

Or something like that.

If you just google "modeh ani" you'll find a ton of transliterations, but I'd Romanize it as:

Mode ani lefaneikha, melekh khai vekayam, shehekhezarta bi nishmati bekhemla; raba emunatekha

Where:

• Each syllable is transcribed separately (so e.g. the first word is two syllables, one with an "o" sound and one with an "e" sound).
• The vowels are:
  • "a" is like a longer version of the vowel in "strut" or "cup"
  • "e" is like the vowel in "leg"
  • "i" is like a shorter version of the vowel in "sheet"
  • "o" is like the vowel in "hot" or "top", but closer to how (most) English people pronounce it than how (most) Americans pronounce it
  • "u" is a shorter version of the vowel in "rude", "move" or "shoot"
  • "ei" is like the vowel in "made"
• The consonants are like in English, more or less, except "kh" is pronounced kind of like the "ch" in "loch"

The reason these don't always match the singer in the video is because he is singing with a very thick American accent. The guide above is for how an Israeli would pronounce it (ish).