According to Dr Sharib:

'Al-Basit is the One Who widens and expands the means of subsistence for
whomsoever He likes and whenever He likes.'

'To emulate the name you should offer thanks to Allah for His sustenance and
for His various and multifarious blessings.'

Appropriate invocation is said to enable a person to be placed in more affluent

see 'The 99 Most Beautiful Names of Allah' by Dr Zahurul Hassan Sharib

Some other references:

Al-Ghazalli refers to Al-Qabid (the Contractor) and Al-Basit (the Expander)
together. He points out that He, God, appropriates alms for the poor from the
rich and extends sustenance to the weak. He also extends sustenance to the
rich until no need remains and witholds sustenance from the poor until no
strength is left.

He also says that among men the one who expands hearts is the one who
inspires by his wise speech.  

(Al-Ghazali - The Ninety-nine Beautiful Names of God. Trans. Burrel/Daher: ITS: 1992.)

Spiritual expansion serves the purpose of reminding the seeker on the Way, of
his goal, it renews the energy and enthuses him to continue his service to
mankind - which leads to the purification of the soul and the pleasure of God.
Such expansion is most readily acquired through the blessings of the spiritual
guide and the close contact with the 'friends of God'. They may inspire by
words, or by a look, or by other means.

With regard to material wealth it is advisable to accept that Al-Qabid and
Al-Basit imply that God distributes material wealth as He sees fit for His purpose
- to accept this with gratitude and to concentrate on the proper use of whatever
material resources are available to one, to the benefit of all.

Bismillah ir Rehman ir Rahim
Qur'an 13:26 (a derived Name)
The Expander,
The One Who Provides Means of Subsistence as He Wills,
The Rejoinder, The Spreader
Allah doth enlarge, or grant
By (strict) measure the Sustenance
(Which He giveth) to whom so
He pleaseth. (The worldly) rejoice
In the life of this world:
But the life of this world
Is but little comfort
Compared to the Hereafter.
'Allaahu yabsutur-Rizqa
limany-yashaaa-'u wa
yaq-dir-Wa farihuu
bil-ha-yaatid-dunyaa. Wa
fil-'Aakhi-rati 'illaa mataa'.

(Qur'an 13: 26)