Honestly, like 90% of this write-up came from one fantastic article if you can read Japanese with some ease I’d suggest you read that one instead of my English write-up, the article is fantastic! (Also, another great article for some similar keigo with great expressions on comparisons from the same site is this one
It is a respectful term for 「行く」, 「来る」and「居 る」. It is also used as a honorific term for 「ある」and「いる」. Because it has varied meaning, it’s important to understand the usage by context.
Due to 「いらっしゃる」having several possible meanings it is very important to use the correct particle and to add the target word. If used ambiguously the opposite party can infer the exact opposite of what you meant.
Note : When using 「いらっしゃる」as an honorific expression for the auxilary verbs 「ある」and「いる」that it expresses a higher level of respect.
Difference from おられる
There is another word similar to 「いらっしゃる」, namely 「おられる」. 「おられる」is the result of appending the auxilary verb 「れる」to 「居る」. It can be said to be a quasi-synonym of 「いらっしゃる」in the sense of being (居る).
(A) お客様は応接室におられます。 (The guests are in the reception room)
(B) 事務所におられるのを見かけました。(I saw you at the office)
The main advantage of using 「おられる」over 「いらっしゃる」is that it helps to avoid ambiguity.
Using 「いらっしゃる」as a replacement for 「行く」
(A) どちらへいらっしゃいますか？ (Where are you going?)
(B) 昨日は大阪までいらっしゃったようですね。(You went to Osaka yesterday, didn’t you?)
セミナーは 来月に予定しております。ぜひご一緒にいらっしゃいませんか。(The seminar is scheduled for next month. Please come with us.)
お伝えしたいことがございますので、受付までいらしてください。(I have something to tell you, so please come to the reception.)
In order to accurately convey the meaning of 「いく」it is important to add a word that describes the destination. If you want to ask the person to “go” somewhere, you can (should?) often change the form to 「いらしてください」.
Using 「いらっしゃる」as a replacement for 「来る」
社長がこちらまでいらっしゃいます。(The president is on his way here.)
イギリス から時間をかけていらっしゃいました。(He took the time to come from England.)
先ほど連絡があり、明日の10時にいらっしゃるとのことです。(He just got in touch with me, he said he will be there tomorrow at 10:00.)
Note : It is important to add where you are leaving from and where you are arriving to avoid confusion with other meanings.
Using 「いらっしゃる」as a replacement for 「居る」
〇〇様はいらっしゃいますか？(Is Mr. 〇〇 here?)
社長がここにいらっしゃると心強いです。(It is reassuring to know that the president is here.)
どうぞ、その場所にいらっしゃってください。(Please come to the place. Note: Especially handy for extra-formal drug hand-offs ^^)
As noted above, if it is difficult to convey the meaning, you can always use 「おられる」.
Using 「いらっしゃる」as a replacement for 「ある」or「いる」
お客様は大変喜んでいらっしゃいました。(The customer was very pleased.)
いつもお美しくていらっしゃる。(You always look so beautiful.)
あそこに座っていらっしゃるのが先生です。(The person sitting over there is the teacher.)
いつまでもお元気でいらっしゃいますね。(I hope you will always be in good health.)
Note : It is combined here with either the 「で」particle or as the conjunctive form of an adjectival verb.
If the context is likely to be construed as misleading there are a lot of quasi-synonyms to clear up the meanings, namely :
For 「行く」meanings : 「行かれる」or「おいでになる」
For 「来る」meanings : 「おいでになる」,「お見えになる」and「お越しになる」
For 「居る」meanings : 「おいでになる」and「おられる」
Differences between 「いらっしゃる」and 「お-になる」
「おいでになる」also has the「行く」,「来る」and「居る」meanings that 「いらっしゃる」has, but it has a more respectful connotation. Both can be used interchangeably, but you would use 「おいでになる」when you want to show more respect.
お客様はまもなくこちらへおいでになります。(The customer will be here shortly.)
発表会にはもうおいでになりましたか？ (Have you been to the presentation yet?)
社長は本日、会社においでになります。(The president is coming to the office today.)
Differences between 「いらっしゃる」and 「お越しになる」
While 「お越しになる」technically also has the 「行く」meaning, it is more often used for its 「来る」meaning. It is easier to understand the “coming” meaning than 「いらっしゃる」and can be used to emphasize the fact that you are coming. The interpretation of using 「お越しになる」over 「おいでになる」is that you appreciate the effort to come more (that they are going out of their way to come).
披露宴は11時から始まりますので、ぜひ皆様でお越しください。(The reception will start at 11:00 a.m., so please come with everyone.)
本日はお寒いなか、お越しくださいましてありがとうございます。Thank you for coming despite it being so cold.)
明日まで展示しておりますので、ぜひお越しくださいませ。(The exhibition will be open until tomorrow, so please do come.)
Differences between 「いらっしゃる」and「お見えになる」
「お見えになる」also means to come, but seemingly used almost exclusively towards “untouchable” (god-like) figures. (e.g. the imperial family, politicians, scholars, doctors, customers …). It is a respectful term that refers to the arrival of a superior, however, it shouldn’t be used for one of your superiors (as in your boss). If you have a good relation with your boss you could use 「いらっしゃる」 , but in most cases one would err on the safe side and use 「お見えになる」 .
A note on 二重敬語
some 二重敬語 (redundant keigo) can be found in the wild with many of these grammar points. People use it to elevate someone to an even higher position, and while technically incorrect, it is used often enough (daily by some) that it could be considered correct.