אנחנו בוחרים בגישור בגלל שהוא יכול לעזור.

בוחרים is the present-tense plural form of לבחור (to choose).

So:

• אנחנו בוחרים = we choose
• It can also mean we are choosing, depending on context

Hebrew present tense often covers both the English simple present and present progressive.

In the present tense, Hebrew often keeps the subject pronoun because the verb form does not clearly show person.

בוחרים tells you the subject is plural masculine/mixed, but by itself it could mean:

• we choose
• you (plural masculine/mixed) choose
• they choose

So adding אנחנו makes it clear that the subject is we.

Because the verb לבחור is commonly used with the preposition ב־ when it means to choose / opt for something.

So:

• לבחור בגישור = to choose mediation / opt for mediation
• לבחור בתוכנית הזאת = to choose this plan

Here, ב־ is not really best understood as the normal English preposition in. It is part of the pattern of the verb. A good way to learn it is as a chunk:

לבחור ב־ = to choose / opt for

גישור means mediation.

It is a masculine singular noun in Hebrew. That matters because later words referring back to it must match its gender and number.

That is why the sentence uses:

• הוא = masculine singular
• יכול = masculine singular

Both refer back to גישור.

In Hebrew, nouns have grammatical gender, and pronouns agree with that gender.

Since גישור is masculine singular, Hebrew refers back to it with:

• הוא = he / it for masculine singular nouns

So although English says it can help, Hebrew says literally:

• הוא יכול לעזור = he/it can help

For non-human things, Hebrew still uses הוא or היא, depending on the noun’s gender.

Because the subject of that part of the sentence is הוא — that is, גישור — and גישור is masculine singular.

So:

• הוא יכול לעזור = it can help

If the subject were we, then it would be plural:

• אנחנו יכולים לעזור = we can help

So יכול agrees with גישור, not with אנחנו.

בגלל means because of.
When Hebrew uses it before a full clause, it often appears as בגלל ש־ (because).

So this part:

• בגלל שהוא יכול לעזור

can be understood as:

• because it can help

Literally, it is something like:

• because that it can help

In everyday Hebrew, this structure is very common.

Yes. A very natural alternative is:

• אנחנו בוחרים בגישור כי הוא יכול לעזור.

That also means We choose mediation because it can help.

A quick comparison:

• כי = very common, neutral because
• בגלל ש־ = also common; often feels a bit like because / due to the fact that
• מפני ש־ = more formal/literary because

So in everyday speech, כי is often the simplest alternative.

Because גישור is being used in a general sense: mediation as a method or approach.

So:

• אנחנו בוחרים בגישור = We choose mediation

If you meant a specific mediation process, you would make it definite, for example:

• אנחנו בוחרים בגישור הזה = We choose this mediation process
• אנחנו בוחרים בגישור המסוים הזה = We choose this specific mediation

Here the sentence is talking about mediation in general, so no the is needed.

Hebrew usually expresses can with a form of יכול plus an infinitive.

So:

• יכול = can / able to (masculine singular)
• לעזור = to help

Together:

• יכול לעזור = can help

More examples:

• אני יכול לעזור = I can help (male speaker)
• אני יכולה לעזור = I can help (female speaker)
• הם יכולים לעזור = They can help

So in your sentence, הוא יכול לעזור literally means it is able to help.

The given sentence is natural, but Hebrew can also rearrange it.

For example:

• אנחנו בוחרים בגישור בגלל שהוא יכול לעזור.
• אנחנו בוחרים בגישור כי הוא יכול לעזור.
• בגלל שהוא יכול לעזור, אנחנו בוחרים בגישור.

All of these are natural. The meaning stays basically the same; the difference is mostly in emphasis and style.

Putting the reason first:

• בגלל שהוא יכול לעזור, אנחנו בוחרים בגישור

gives a bit more emphasis to the reason.