The recommended precaution is that in prayers one should not stop on a letter that has a vowel nor join a letter that has a sukūn. The meaning of stopping on a letter that has a vowel is that one pronounces the fatḥah, kasrah, or ḍammah of the last letter in a word and then pauses between that word and the next.
For example, when he recites الرَّحْمَـٰنِ ٱلرَّحِيْمِ [arraḥmānir rahīm], he pronounces the kasrah of the letter mīm [م] in الرَّحِيْمِ [arraḥīm, so that it is pronounced ‘arraḥīmi’], and then pauses briefly before reciting the next verse مٰلِكِ يَوْمِ الدِّيْنِ [māliki yawmid dīn]. The meaning of joining a letter that has a sukūn is that one does not pronounce the fatḥah, kasrah, or ḍammah of the last letter in a word and then joins that word with the next.
For example, when he recites الرَّحْمَـٰنِ ٱلرَّحِيْمِ [arraḥmānir rahīm], he does not pronounce the kasrah of the letter mīm [م] in الرَّحِيْمِ [arrahīm], and then immediately recites مٰلِكِ يَوْمِ الدِّيْنِ [māliki yawmid dīn].