According to Dr Sharib:

"Al-Latif is the One Who knows fully well the 'pros and cons' and the 'how and
why' of all things. He confers and bestows blessings and the choicest of things
on people. He has no beginning and no end. His wisdom cannot be fathomed.
According to some Al-Latif is the One Who removes the troubles and the
sorrows of the people very soon."

Dr Sharib also points out another understanding, which is that Al-Latif is the
One Who hides one thing in another, or in other words He covers things so that
their true nature is not obvious. He gives the example of the Prophet Yusuf
(Joseph) whose true nature was hidden for long in the veil of slavery.

To emulate the name you should show utmost courtesy and kindness to the
people and guide them to the path of truth and righteousness without
intimidation or coercion. You should be an example of better living, better
morals, and elevated ideals.

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

Some other references:

Al-Ghazali emphasises the benevolence of God that, he says, involves the
combination of gentleness in action with a delicacy of perception. The actions
of God as reflected in the natural processes of the world give a hint of this
quality. The marvelous unfolding of a child with each stage of its development
from a foetus, and the intricate combination of factors manifesting at the right
time and in the right way are one of the many examples he gives. In modern
terms he might have pointed out the way that the hidden pattern within the DNA
of each individual becomes gradually revealed as the whole functioning human
with its higher faculties.

He also places this attribute within the context of other names:

"...He (God) is wise in so far as He plans things, generous in so far as He
orders them, just in so far as He puts each thing in its proper place, and
benevolent in so far as He does not overlook subtleties and qualities of
gentleness concerning them."

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

At the beginning of the Mesnevi Mevlana Jalaluddin Rumi has the reed pipe,
that has been separated from the reed bed, lament that:

"My secret is not far from my plaint, but eye and ear lack the light whereby it
should be apprehended.

Body is not veiled from soul nor soul from body, yet none is permitted to see
the soul."

Mevlana Jalaluddin Rumi: Masnavi: Book 1. 7/8

Subtle qualities are hidden within man, but are concealed by God from the
perception of most individuals. To put it another way - man's potential is great
but is subtle and is thus hidden by and within man's coarser nature.

Bismillah ir Rehman ir Rahim
The Subtle, The Gracious, The Most Pleasant,
The Benevolent
Qur'an 42:19
Gracious is Allah
To His servants:
He gives Sustenance
To whom He pleases:
And He is the Strong,
The Mighty.
'Allahu Latiifum-bi-'ibaadihii yarzuqu
many-yashaaa': wa

(Qur'an 42:19 trans. Y. Ali)