jazaakAllaahu khayraa.
One of the most popular & perhaps, one of the most important hadeeth regarding Ramadan is that which says:
(( من صام رمضان إيماناً واحتساباً غفر له ما تقدم من ذنبه، ومن قام رمضان إيماناً واحتساباً غفر له ما تقدم من ذنبه، ومن قام ليلة القدر إيماناً واحتساباً غفر له ما تقدم من ذنبه ))
Which mentions the forgiveness of previous sins for the one who, in Ramadan, fasts / stands in prayer "إيماناً واحتساباً" (eemaanan wa-htisaabaa) [sometimes translated as: "having faith & hoping for the reward"].
In this short Q & A, Shaykh 'Ubayd - may Allah preserve him - explains the meaning of this phrase. May Allah help us to learn it and act upon it - so that we attain His forgiveness - and also teach it to others.