Praise be to Allah.

This hadeeth was narrated by at-Tirmidhi (2442), Ahmad (1630) and Ibn Hibbaan (722) from al-Hasan ibn ‘Ali (may Allah be pleased with him) who said: I memorized from the Messenger of Allah (blessings and peace of Allah be upon him): “Leave that which makes you doubt for that which does not make you doubt, for truth leads to reassurance and lies lead to uncertainty.” Classed as saheeh by Shaykh al-Albaani (may Allah have mercy on him). 

It was also narrated by an-Nasaa’i (5614) without the additional words “for truth leads to reassurance…” 

Al-Mannaawi (may Allah have mercy on him) said: “Leave that which makes you doubt” means: refrain from that which you are uncertain as to whether it is good or bad, halaal or haraam

“for that which does not make you doubt” that is: turn instead to that about which you are not uncertain, that which you are sure is good and halaal.

“for truth leads to reassurance” means: the heart is at ease with it

“and lies lead to uncertainty” means: they make the heart anxious and uneasy. At-Teebi said: This phrase explains the preceding words. What it means is: if you find yourself doubting (and uncertain about) something, then leave it, for the heart of the believer is at ease with the truth and is doubtful about lies and falsehood. Being doubtful about something is an indication that it may be false and wrong, so beware of it; and your feeling at ease with something is an indication that it is true, so take hold of it.

End quote from Fayd al-Qadeer 3/529 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: This hadeeth is an example of concise speech, and how excellent and beneficial it is to follow it. One may feel doubtful about many things, so we say: leave that which you have doubts about for that which you have no doubts about, so that you may be safe and sound. If anything makes you feel doubtful and anxious, then leave it for something that does not make you feel doubtful, so long as this does not reach the level of waswaas (when you start doubting everything). If it does reach the level of waswaas, then do not pay any attention to it. 

This has to do with acts of worship, interactions with others, marriage and all categories of knowledge. 

An example of that in the case of acts of worship is that of a man who breaks his wudoo’, then prays, and he is not sure whether he did wudoo’ after breaking it or not. He is unsure, because if he did do wudoo’ then his prayer is valid, but if he did not then his prayer is invalid, so he remains anxious. In this case we say: Leave that which makes you doubt for that which does not make you doubt. The doubt in this case has to do with whether the prayer was valid and not doubting means that you should do wudoo’ and pray. 

The opposite of the previous example is that of a man who does wudoo’ then prays, and he is not sure whether he broke his wudoo’ or not. 

In this case we say: Leave that which makes you doubt for that which does not make you doubt. You have something which is certain, which is that you did wudoo’, then you were not sure whether this wudoo’ was broken or not. What you should ignore is the doubt or uncertainty as to whether the wudoo’ was broken or not. So calm down and ignore that doubt or uncertainty.

End quote from Sharh al-Arba‘een an-Nawawiyyah, p. 155 

This hadeeth is a basic principle in the area of being prudent and is encouragement to ignore doubts. It is also a basic principle in the area of following that which is certain and ignoring that which is dubious. 

Al-Haafiz Ibn Rajab (may Allah have mercy on him) said:

This hadeeth highlights the importance of being careful when faced with doubtful and dubious matters, and keeping away from them, because in the case of that which is definitely halaal, the believer will have no doubt in his heart concerning it – and doubt here means anxiety and worry – rather he will feel at ease and will have reassurance in his heart. As for that which is doubtful, he will feel anxiety and worry concerning it.

End quote from Jaami‘ al-‘Uloom wa’l-Hukam, 1/280 

And Allah knows best.