ordentlich
neat
Tidy, clean, and well organized. The opposite of messy or chaotic.
Sein Schreibtisch ist immer sehr ordentlich.
His desk is always very neat.

neat / proper
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neat
Tidy, clean, and well organized. The opposite of messy or chaotic.
Sein Schreibtisch ist immer sehr ordentlich.
His desk is always very neat.

The adjective 'ordentlich' (neat/proper) is derived from the noun 'die Ordnung' (order). Everything that is 'ordentlich' has some form of order or structure.
Nachdem sie aufgeräumt hatte, war ihr Zimmer wieder ordentlich.
After she had tidied up, her room was neat again.
The meaning of 'ordentlich' depends strongly on the context. If it refers to a room, it means 'aufgeräumt' (tidy). If it comes before a noun like 'Spaß' (fun) or 'Hunger' (hunger), it means 'viel' (a lot). In formal documents, it often means 'regelkonform' (compliant with the rules).
Bitte füllen Sie das Formular ordentlich aus.
Please fill out the form properly.
In colloquial speech, 'ordentlich' is often used as an adverb to intensify an amount or degree. It then means 'sehr' (very) or 'viel' (a lot) and is not declined.
Das hat ordentlich Geld gekostet.
That cost quite a lot of money.
In formal or legal contexts, 'ordentlich' is part of fixed terms. Examples are 'ordentliches Mitglied' (full member) or 'ordentlicher Professor' (full professor/chair holder).
Er wurde zum ordentlichen Professor an der Universität berufen.
He was appointed full professor at the university.
very
'sehr' and 'ordentlich' can both express strong intensity. 'sehr' is neutral and can be used with many adjectives, adverbs, and some verbs. 'ordentlich' in this meaning is colloquial and means roughly 'quite strongly' or 'quite a lot'. It fits especially well when something is noticeable or clear, for example with work, rain, hunger, or effort. Important: 'ordentlich' can also mean 'neat' or 'proper'. As an intensifier, it sounds more casual than 'sehr'.

Beim Umzug haben wir ordentlich geschwitzt.
We worked up quite a sweat during the move.
Ich bin heute sehr konzentriert, weil die Prüfung bald beginnt.
I am very focused today because the exam is about to start.