Praise be to Allah.
Obligatory is that which the Lawgiver has enjoined by way of it being compulsory.
Examples include the five daily prayers, fasting Ramadan, zakaah for those who are obliged to give it, and Hajj to the Sacred House for those who have the means of doing so.
That which is obligatory may be called waajib, fard, and so on. The one who does it will be rewarded for obeying the command and the one who does not do it deserves to be punished.
Encouraged or recommended is that which is prescribed by the Lawgiver, but not by way of it being obligatory or compulsory.
Examples include qiyaam al-layl, the regular Sunnah prayers that are additional to the five obligatory prayers, fasting three days of every month, fasting six days of Shawwaal, giving charity to the poor, and regularly reciting adhkaar and awraad.
That which is recommended may be called mustahabb, Sunnah, masnoon or naafil. The one who does it will be rewarded for complying, but the one who does not do it will not be punished.
Prohibited or forbidden is that which the Lawgiver prohibits in the sense that it is obligatory to refrain from doing it.
Examples include zina (fornication or adultery), riba (usury), drinking alcohol, disobedience to parents, shaving off the beard, and making a wanton display (in the case of women).
The one who refrains from doing that which is prohibited will be rewarded for complying, and the one who does it deserves to be punished.
Disliked is that which the Lawgiver disallowed, but not in the sense of it being obligatory to refrain from it.
Examples include giving and taking with the left hand; women following funeral processions; conversing after ‘Isha’; praying in a single garment of which no part is over the shoulder; offering supererogatory prayers after Fajr until the sun is fully risen, or after ‘Asr until the sun has set.
The person who refrains from a disliked action will be rewarded for complying, but the one who does it will not be punished.
Permissible is that to which no command or prohibition is connected to the deed itself.
Examples include: eating and drinking; buying and selling; travelling for the purpose of tourism or seeking provision; engaging in intimacy with spouses during the night in Ramadan.
The restriction on the definition of what is permissible is indicated by the phrase “To the deed itself”, because there may be an instruction that is connected to it, which makes it enjoined or disallowed.
In principle, buying water is permissible, but if doing wudoo’ for an obligatory prayer depends on that, then it becomes obligatory to buy it, because that without which an obligatory duty cannot be completed also becomes obligatory.
In principle, travelling for the purpose of tourism or leisure is permissible, but if that travel is to a land of the disbelievers in which there is a great deal of temptation and evildoing, and immorality is widespread, then that travelling becomes prohibited, because it is a means that leads one to falling into that which is unlawful.
For more information, please see the following books:
Rawdat an-Naazir wa Jannat al-Manaazir by Ibn Qudaamah (1/150-210)
Al-Bahr al-Muheet by az-Zarkashi (1/140-240)
Sharh al-Usool min ‘Ilm al-Usool by Ibn ‘Uthaymeen (p. 46-68)
And Allah knows best.