Sistem verileri hızlı işliyor.

The -i here is the accusative case marker, which often marks a definite or specific direct object in Turkish.

• veriler = data / the data in a general plural sense
• verileri = the data as the specific thing being processed

So in this sentence, verileri is the object of işliyor and means the system is processing those specific data.

It can be ambiguous in Turkish.

Depending on context, verileri can mean:

• the data (plural + accusative)
• his/her/its/their data in some contexts

In this sentence, the most natural reading is usually the data because it fits the structure subject + object + verb very well:

• Sistem = subject
• verileri = object
• işliyor = verb

So unless the wider context says otherwise, a learner should usually understand it here as the data.

Yes, hızlı is basically an adjective meaning fast or quick, but in Turkish, many adjectives can also be used adverbially without changing form.

So:

• hızlı sistem = a fast system
• hızlı işliyor = it processes quickly / fast

This is very common in Turkish. English usually distinguishes fast and quickly, but Turkish often does not need a separate adverb form.

You could also hear:

• hızlıca işliyor = processes quickly
• hızla işliyor = processes rapidly

But hızlı işliyor is normal and natural.

İşliyor comes from the verb işlemek.

In this sentence, işlemek means to process.

So:

• işlemek = to process
• işliyor = is processing / processes

This verb has several meanings in Turkish depending on context, but with veri / veriler it commonly means to process data.

İşliyor is the present continuous form of işlemek.

The structure is:

• verb stem: işle-
• present continuous suffix: -iyor
• result: işliyor

What happens is that the final vowel in the stem often changes or drops when -iyor is added, so işle- + -iyor becomes işliyor.

This form can mean:

• is processing right now
• processes in a general present sense, especially in descriptive or technical statements

By contrast:

• işler is the aorist and often means works / functions / processes in a more general, habitual, or timeless way

So:

• Sistem verileri işliyor = The system is processing / processes the data
• Sistem verileri işler = The system processes data / would process data in a more general or formal sense

Because Turkish normally puts the verb at the end.

A very common neutral Turkish order is:

Subject + Object + Adverb + Verb

So here:

• Sistem = subject
• verileri = object
• hızlı = adverbial element
• işliyor = verb

That gives:

Sistem verileri hızlı işliyor.

Turkish word order is flexible, but this version sounds natural and straightforward.

Turkish does not have articles like the and a/an in the same way English does.

So sistem can mean:

• the system
• a system
• sometimes just system in a general sense

Context tells you which one is meant.

If Turkish wants to make a system clearer, it can use bir:

• Bir sistem verileri hızlı işliyor. = A system processes the data quickly.

Without bir, sistem is often understood as the system or as a general subject, depending on context.

You might hear different word orders in Turkish, but they do not all sound equally natural.

• Sistem verileri hızlı işliyor. → natural
• Sistem hızlı verileri işliyor. → usually sounds like hızlı is describing verileri, which does not make much sense here
• Sistem verileri işliyor hızlı. → unnatural in normal standard Turkish because the verb usually comes last and the adverb normally comes before it

So if you want quickly to describe the action, hızlı should stay close to the verb:

• Sistem verileri hızlı işliyor.

In Turkish, veri is the basic noun and often corresponds to English data in a general sense.

• veri = data / a datum depending on context
• veriler = data sets / pieces of data / data explicitly plural
• verileri = the data as a specific plural object

In technical Turkish, veri is often used much like English mass-noun data, so learners should not expect a perfect one-to-one match with English singular/plural usage every time.